Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with N=2 diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional nondiffusing species. Here we ask whether this diffusive threshold lowers for N>2 to allow "true" Turing instabilities. Inspired by May's analysis of the stability of random ecological communities, we analyze the probability distribution of the diffusive threshold in reaction-diffusion systems defined by random matrices describing linearized dynamics near a homogeneous fixed point. In the numerically tractable cases N≤6, we find that the diffusive threshold becomes more likely to be smaller and physical as N increases and that most of these many-species instabilities cannot be described by reduced models with fewer species.

中文翻译：

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随机反应扩散系统中的图灵扩散阈值

仅当化学物质的扩散度足够不同时，才会出现反应扩散系统的图灵不稳定性。这个阈值在大多数具有N = 2扩散物质的系统中是不自然的，从而迫使实验性的不稳定性依赖于波动或其他非扩散物质。在这里，我们问这个扩散阈值是否在N> 2时降低，以允许“真实的”图灵不稳定性。受到May对随机生态群落稳定性的分析的启发，我们分析了由随机矩阵定义的反应扩散系统中扩散阈值的概率分布，该随机矩阵描述了均质固定点附近的线性动力学。在数值易处理的情况下，N≤6，